Joint User Scheduling and Hybrid Beamforming Design for Massive MIMO LEO Satellite Multigroup Multicast Communication Systems

. 2022 Sep 10;22(18):6858. doi: 10.3390/s22186858

Algorithm 1: Joint user scheduling and hybrid beamforming design algorithm.

Input: CCCP algorithm iteration index

k

, thresholds

ε_{1}

, penalty iteration algorithm iteration index

m

, thresholds

ε_{2}

, penalty factor

λ_{1}

λ_{2}

λ_{3}

.
1. Initial:

{(η, W, S I N R_{l}^{\min}, ζ)}^{(k = 0)}

q^{(k = 0)}

.
2. while

|{EE}^{(k)} - {EE}^{(k - 1)}| \geq ε_{1}

3. Convexification step by (57), (59), (61).
4. Calculation

q^{(k)}

, substitute

q^{(k)}

into (77).
5. Optimization step.
6. Let

{(η, W, S I N R_{l}^{\min}, ζ)}^{(m = 0)} = {(η, W, S I N R_{l}^{\min}, ζ)}^{(k = 0)}

.
7. while

|{\{T r (W_{l}^{(m)}) - λ_{\max} (W_{l}^{(m)})\}}_{l = 1}^{L}| \geq ε_{2}

8. Calculate the maximum eigenvalue

λ_{\max} (W_{l})

W_{l}^{(m)}

and the corresponding eigenvector

w_{l, \max}^{(m)}

.
9. Using CVX toolbox, calculate the variables

{(η, W, S I N R_{l}^{\min}, ζ)}_{o p t}^{(m)}

at the

m th

iteration according to (77).
10. If

{\{W_{l}^{(m + 1)}\}}_{l}^{L} \approx {\{W_{l}^{(m)}\}}_{l}^{L}

, then
11. Update

λ_{3} = 2 λ_{3}

.
12. else
13. Update

m = m + 1

.
14. end
15. end
16. Update

{(η, W, S I N R_{l}^{\min}, ζ)}^{(k + 1)} = {(η, W, S I N R_{l}^{\min}, ζ)}^{(m)}

k = k + 1

λ_{1} = λ_{1} + 1

λ_{2} = λ_{2} + 1

.
17. end
Output:

{(η, W, S I N R_{l}^{\min}, ζ)}_{o p t}^{}